First experimental determination of the $^{40}$Ar($n,2n$)$^{39}$Ar reaction cross section and $^{39}$Ar production in Earth's atmosphere

TL;DR

This study addresses the uncertainty in atmospheric $^{39}$Ar caused by cosmogenic production by experimentally measuring the total cross section of the dominant channel $^{40}$Ar$(n,2n)^{39}$Ar at $E_n \approx 14.8$ MeV. Using 14.8 MeV neutrons from a DT generator, two independent detection methods (NOGAMS and LLC) quantify $^{39}$Ar production in $^{40}$Ar-enriched gas, yielding a cross section of $610 \pm 100$ mb and validating modern theories, including TALYS-2.00 and ENDF/B-VIII.1. These cross sections, combined with cosmic neutron spectra, give a sea-level production rate of $P \approx 744-770$ atoms kg$^{-1}$ Ar day$^{-1}$ and a secular equilibrium $^{39}$Ar/Ar of $(5.9 \pm 1.8) \times 10^{-16}$, implying about 73% of atmospheric $^{39}$Ar is cosmogenic. The remaining ~20% arises from anthropogenic DT-neutron exposure during nuclear tests, highlighting the significance of accurately quantifying neutron-induced production for dating applications and environmental monitoring.

Abstract

The cosmogenic $^{39}$Ar(t$_{1/2}$= 268 years) isotope of argon is used for geophysical dating and tracing owing to its appropriate half-life and chemical inertness as a noble gas; $^{39}$Ar serves also in nuclear weapon test monitoring. We measured for the first time the total cross section of the main $^{39}$Ar cosmogenic production reaction in the atmosphere, namely $^{40}$Ar$(n,2n)^{39}$Ar, using 14.8$\pm0.3$ MeV neutrons. The neutrons, produced by a deuterium-tritium generator, impinged on a stainless steel sphere filled with Ar gas highly enriched in the $^{40}$Ar isotope. The reaction yield was measured by atom counting of $^{39}$Ar with noble gas accelerator mass spectrometry and, independently, by decay counting relative to atmospheric argon. A total $^{40}$Ar$(n,2n)^{39}$Ar cross section of 610$\pm100$ mb was determined. This result serves as a benchmark for recent theoretical calculations and evaluations, found to reproduce well the experimental total cross section. We use these energy-dependent theoretical cross sections together with experimental spectra of cosmogenic neutrons at different altitudes to calculate the global average rate of neutron-induced $^{39}$Ar atmospheric production, resulting in $770\pm240$ $^{39}$Ar atoms/cm$^2$/day. The secular equilibrium between the $^{39}$Ar calculated production rate and radioactive decay rate leads to a partial isotopic abundance $^{39}$Ar/Ar$= (5.9\pm 1.8) \times 10^{-16}$, showing that $\approx$73% of atmospheric $^{39}$Ar is produced by cosmogenic neutrons. The $^{40}$Ar($n,2n$)$^{39}$Ar cross section at 14 MeV is also a key parameter for quantifying the anthropogenic contribution to atmospheric $^{39}$Ar produced during the thermonuclear tests of the 1960s. We estimate that anthropogenic $^{39}$Ar accounts for roughly 20% of the present atmospheric inventory.

Figures (6)

• Figure 1: Photograph of (a) $^{40}$Ar-filled sphere used for activation at the TUD DT neutron generator; (b) activation setup (from left to right): accelerator beam pipe ending with the beam stop holding the tritium target, two rows of (light grey) rectangular neutron absorbers, the 20 mm diameter sphere sandwiched between Al, Zr and Nb monitor foils of same diameter. The sphere is positioned at 10 cm from the beam stop holding the tritium target.
• Figure 2: Schematic diagram of: (a) the Noble Gas Accelerator Mass Spectrometry setup at Argonne National Laboratory for $^{39}$Ar detection. $^{38,39,40}$Ar$^{8+}$ ions are sequentially injected from the Electron Cyclotron Resonance (ECR-III) ion source and accelerated through the Positive Ion Injector (PII) and Booster- and ATLAS-Linac. Intensity of stable isotope $^{38,40}$Ar$^{8+}$ accelerated beams are measured as charge current (typically of the order of nA) in an electron-suppressed Faraday Cup (FC). The rare isotope $^{39}$Ar is counted as individual ions in the Enge Gas-Filled Magnetic spectrograph (GFM); (b) the multi-anode plate of the Monica ionization chamber CAL22shrt located perpendicular to the focal plane of the GFM. Energy loss signals for ions entering the detector are extracted from each anode A1-A8 for identification. The position P23 along the GFM dispersion axis is measured by the normalized difference of signals in the split anodes A2 and A3 (P23= (A3-A2)/A3+A2)).
• Figure 3: Identification spectrum of $^{39}$Ar ions in the detector measured for: (top left) the diluted SNRC sample irradiated at Soreq NRC; (top right) a non-irradiated atmospheric Ar sample ($^{39}$Ar/Ar= $8.12\times 10^{-16}$) where $^{39}$Ar is below detection sensitivity; (bottom) the HZDR (2022) irradiated sample. The horizontal axis represents the dispersion along the focal plane and the vertical axis represents the differential energy loss signal measured in the fourth anode of the focal-plane ionization chamber. The upper and lower left-hand groups originate from $^{39}$K$^{8+}$ (stable isobar of $^{39}$Ar) and $^{34}$S$^{7+}$ ions, respectively, both chemical impurities in the ion source. $^{34}$S$^{7+}$ ions are nearly degenerate in $m/q$ with $^{39}$Ar$^{8+}$.
• Figure 4: Cross section of the $^{40}$Ar$(n,2n)^{39}$Ar reaction measured by AMS (open symbols) and LLC (solid symbols). The error bars represent 1$\sigma$ uncertainty derived from repeat measurements in each experiment. The adopted unweighted mean and standard deviation (dashed lines) of the measured cross section values are shown.
• Figure 5: Cross section (left axis) of the $^{40}$Ar$(n,2n)^{39}$Ar and $^{40}$Ar$(n,pn)^{39}$Cl reactions calculated by the ENDF/B-VIII.1 evaluation and the TALYS-2.00 code as a function of neutron energy. Our experimental value and the 1$\sigma$ uncertainty for the $^{40}$Ar$(n,2n)^{39}$Ar cross section at 14.8 MeV is plotted. The insert shows the region around the experimental point in linear scale. Experimental spectra (right axis) of neutron flux of cosmic origin at sea-level are also plotted.